Absolute Energy Calibration of X-ray TESs with 0.04 eV Uncertainty at 6.4 keV in a Hadron-Beam Environment

A performance evaluation of superconducting transition-edge sensors (TESs) in the environment of a pion beam line at a particle accelerator is presented. Averaged across the 209 functioning sensors in the array, the achieved energy resolution is 5.2 eV FWHM at Co $K_{alpha}$ (6.9 keV) when the pion beam is off and 7.3 eV at a beam rate of 1.45 MHz. Absolute energy uncertainty of $pm$0.04 eV is demonstrated for Fe $K_{alpha}$ (6.4 keV) with in-situ energy calibration obtained from other nearby known x-ray lines. To achieve this small uncertainty, it is essential to consider the non-Gaussian energy response of the TESs and thermal cross-talk pile-up effects due to charged-particle hits in the silicon substrate of the TES array.